It is common to use same type of inductors for each phase of multi-phase buck converters; it is also common to use a same type of inductors for each phase to maximize the merit of multi-phases, such as better transient response, smaller ripple and less harmonic noise. However, this may not be an optimum solution in terms of efficiency, if one needs higher efficiency over a wide range from light load to heavy load.
It is commonly known that smaller value inductors give faster transient response, and that larger value inductors have low AC losses, which gives high efficiency at light load condition. Mixing different inductance values, sizes and types is not common, and would not give a benefit unless the buck architecture is adapted to using different inductance values.
Multi-operation modes of DC-to-DC converters include sleep mode often pulse-frequency modulation (PFM) mode and sync mode often pulse-width modulation mode (PWM).